Equilibrium position of the system of solids attached to an Euler-Bernoully beam, described by a hybrid system of differential equations

The article considers a refined generalized mathematical model that allows us to describe a wider class of systems of interconnected solids elastically attached to an Euler—Bernoulli beam. The model is described by a non-uniform linear hybrid system of differential equations with coefficients depending on the Dirac delta functions. Nonhomogeneity in the system necessitates finding the initial conditions corresponding to the position of bodies and beam deflection in a state of equilibrium. The equilibrium position of a mechanical system is understood as a solution of the initial hybrid system of differential equations that doesn't vary with time. It is proposed an approach to find the equilibrium position of the system of solids attached to an Euler—Bernoulli beam in the chosen coordinate system.